Baiji Foundation (now vanished, like the species)The Yangtze River dolphin, or baji, is presumed extinct by marine mammal experts.

But most of the time, extinction is happening invisibly, a presumptive consequence of habitat loss and other factors. Now a statistical fight is brewing over the quality of calculations long made to estimate the rate at which species are departing.

They stress that this does not negate the reality of the wave of species loss under way in an increasingly human-dominated planet:

Although we conclude that extinctions caused by habitat loss require greater loss of habitat than previously thought, our results must not lead to complacency about extinction due to habitat loss, which is a real and growing threat.

But their paper strongly challenges longstanding conventions used to estimate vanishings that still mainly occur invisibly. Gaps in understanding of the processes leading to extinction were already raising big questions more than a decade ago, as I reported in this news story in 2000: “Extinction Turns Out to Be a Slow, Slow Process.” I’ve appended a highly relevant excerpt at the bottom of this post.

But Pimm also sent me a strong criticism of the paper by e-mail, calling it a “sham.” I shared his critique with Hubbell, who sent a reply. I’ve appended the exchange below. The discussion will play out in the peer-reviewed literature in the end, but this is a useful rough sketch of the issues. First is Pimm:

The paper is a sham: it does not report extinction rates or the numbers of species that are threatened. Despite its posturing, it deals with a different issue.

The paper is riddled with false statements. For instance, the paper states: “Estimates of extinction rates based on (the species-area) method are almost always much higher than those actually observed.”

It is unequivocally false. One reference used to support this (Pimm and Askins) uses a species-area relationship to predict 4.5 bird extinctions following deforestation in Eastern North America and then notices that four species went extinct and one is threatened. There are dozens of other studies of many taxa around the world that find equally compelling agreements between predicted and observed extinctions. A small selection of them follows.

So what does the paper model — and why does it poorly address the issue of extinctions? Imagine destruction that wipes out 95% of the habitat in an area metaphorically “overnight”. How many species have disappeared “the following morning”? The paper tells you. It is not many, just those wholly restricted to the 95% (and absent from the 5% where they would survive).

The important question is: How many of additional species living lonely lives in their isolated patches (the 5%) would become extinct eventually because their population sizes are too small to be viable? A different species-area curve applies — the one for islands, which are isolated. It is a much larger number of extinctions, of course, and the one used in the studies mentioned above that find such compelling agreement between predicted against observed extinctions.

I am very sorry that Stuart has taken our paper so badly. He is a really good scientist, but our paper is not a sham, it is a mathematical proof. We realized the problem with the method 8 years ago, but we only figured out how to prove it mathematically last year, and we wanted a proof to make it completely clear why the problem was real.

Stuart does not address the fundamental problem with the [species-area relationship] SAR, which is that it only measures areas of first contact with a species, not areas of last contact (i.e., areas that contain the entire range of a species). The fact that he got good agreement is a specific instance (in which the number of predicted species lost is in agreement with the SAR), but this will only happen if the area of habitat destroyed happens to contain the entire ranges of the species that went extinct.

This is only by happenstance in this particular case. However, the backward SAR method does not distinguish between species that are endemic to the area of destroyed habitat and those that are not. His point does not disprove the theorem in our paper. Stuart made a very valuable contribution several years ago by arguing that we ought to focus on species that were in imminent danger of extinction, i.e., those whose ranges were endemic to the area of destroyed habitat.

But the problem is that the SAR is constructed from areas of first contact with species (you only have to find one individual of a new species to increment the species counter), so to run the species-area curve backward to estimate species extinction makes the tacit assumption that a species is committed to extinction when as few as one individual of the species is lost. This is clearly not true.

As a coda, here’s an excerpt from my article on extinction science, which essentially proposes that while debates about extinction rates are important to clear up, they’re perhaps focused too far down the sequence from degradation to disappearance:

A growing group of paleontologists and ecologists are calling for a new push to improve the data behind estimates and to stop making broad statements comparing current events to past cataclysmic extinction spasms like the one that erased the dinosaurs 65 million years ago. Those comparisons, they say, implied a level of clarity in the science that just does not exist. They add that scientists should emphasize that extinction itself happens over a span that is always going to be hard to measure or comprehend.

”In thinking about global extinction we’ve got to free ourselves from this human time scale,” said Dr. John Alroy, an ecologist at the National Center for Ecological Analysis and Synthesis of the University of California at Santa Barbara. ”To a species, a human lifetime is a little flicker.”

Human-caused extinctions are happening, Dr. Alroy said, and he is one of many biologists who are convinced that the pace is rapidly accelerating. It is just that this wave of biological losses is building but has yet to break.

Only in retrospect, when some future culture — human or otherwise — examines the fossil record, will the die-off be evident as a substantial pruning of the branches of the tree of life, he said. ”For the entire remaining duration of life on earth,” he said, ”this event we’re responsible for is clearly going to show up as a signature.”

Instead of focusing on the nearly immeasurable moment when a species ceases to exist, he and other biologists say, science should focus harder on the forces that lead toward extinction — the destruction or fragmentation of habitat, the introduction of invasive species, the appropriation of water or other vital resources. [Read the rest.]

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By 2050 or so, the human population is expected to pass nine billion. Those billions will be seeking food, water and other resources on a planet where humans are already shaping climate and the web of life. Dot Earth was created by Andrew Revkin in October 2007 -- in part with support from a John Simon Guggenheim Fellowship -- to explore ways to balance human needs and the planet's limits.